The father’s lawyer argued the inquest findings should only record her death.

The case is before the Law Lords and Mr Justice Hickenbottom said he would reserve judgement until a later date.

Leslie Thomas QC, who represented Mr Worthington at the inquest in Kendal in December 2017, told the High Court in Manchester earlier that his client was “entitled” to have the inquest’s finding corrected.

Mr Roberts concluded Poppi suffocated at the family home in Barrow as she slept next to her father in an “unsafe sleeping environment”.

But after hearing conflicting evidence of injuries from two pathologists and other experts, he also concluded Mr Worthington sexually assaulted his daughter shortly before her death.

Mr Worthington, who has never been charged, appeared at the inquest but refused to answer 252 questions.

Mr Thomas said the coroner was wrong to list details of the assault on his inquisition, which forms part of the official record, because, according to the law, this should only detail how the child died.

He said: “What is on the record and will be kept on the record, and people tend to go to, is the inquisition, the very end document where the findings are, and that’s incorrect.”

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Mr Thomas added: “It is perfectly clear this was an asphyxia death. (The coroner) has overstepped the mark. (The assault) is irrelevant to how she died.”

Samantha Leek QC, representing the coroner David Roberts, said the assault detail was “the central issue in the inquest” and it would be “completely artificial” to leave it out.

She added: “[Poppi] came by her death because she’s brought into bed to be harmed.”

Mr Worthington is believed to be in hiding following publicity around his daughter’s death.